Given a tree T on n vertices, and k, b, s1, . . . , sb ∈ N, the Tree Partitioning problem asks if at most k edges can be removed from T so that the resulting components can be grouped into b groups such that the number of vertices in group i is si, for i = 1, . . . , b. The case when s1 = · · · = sb = n/b, referred to as the Balanced Tree Partitioning problem, was shown to be NP-complete for tr...
